Method of measuring mechanical data of a soil, and of compacting the soil, and measuring or soil-compaction device

ABSTRACT

Method and apparatus for compacting soil and for determining a mechanical characteristic of soil, including a method and apparatus for periodically compacting soil with a soil compacting device so as to make the soil and the soil compacting device vibrate together as a single oscillatory system, analyzing the vibration of the soil and soil compacting device, and adjusting an oscillatory driving force so as to drive the single oscillatory system towards a characteristic resonance frequency OMEGA.

This application is the national phase under 35 U.S.C. §371 of PCTInternational Application No. PCT/CH97/00396 which has an Internationalfiling date of Oct. 21, 1997 which designated the United States ofAmerica.

FIELD OF THE INVENTION

The invention relates to a method for measuring the mechanical data of agraded and tampered soil, or a soil that is to be graded and tampered,to a grading and tampering method in order to achieve optimal, inparticular, homogeneous grading and tampering of a soil, to an apparatusfor measuring the mechanical data of a graded and tampered soil, or of asoil that is to be graded and tampered, and to an apparatus for gradingand tampering a soil in order to achieve optimal, homogeneous compactingof that soil.

DESCRIPTION OF RELATED ART

A method for soil grading and tampering is known in the art from WO95/10664. With this known method, the frequency of a rotating unbalanceis adjusted in such a way that the grader and tamper unit, which hascontact with the ground that is to be graded and tampered, will notexceed a preset harmonic oscillation value - here twice the value of thefundamental oscillation. Staying below this preset value is defined as astability criterion. Using two acceleration recorders, arrangedvertically to each other on the grader and tamper unit, theiraccelerations are measured. One acceleration recorder measures thehorizontal, the other measures the vertical acceleration component.Determined are the oscillation amplitude of the grader and tamperdevice, and the direction of the maximum compacting amplitude. Thefrequency of the eccentric, as well as its weight and the rolling speedare adjustable with the aid of a computer. However, these values areadjusted in such a way so as to avoid machine and chassis resonance.Adjustment of the eccentric's frequency and weight is carried outwithout accounting for the qualities of the soil that is to be gradedand tampered. Based on the measured acceleration values, the modulus ofelasticity in shear of the compacted soil and its plastic parameter aredetermined.

Another method for soil grading and tampering is known in the art fromEP-A 0 459 062. With this known grading and tampering method, emphasisis placed on adjusting the machine parameters in such a manner thatpreset forces acting upon the the soil, which is to be graded andtampered, are achieved.

SUMMARY OF THE INVENTION

The object of the invention is to describe a method for measuring and/orgrading and tampering a soil, and to create an apparatus for measuringand/or grading and tampering a soil which allows homogeneous soilcompacting by using a grading and tampering method that requires as fewequipment runs as possible; in particular, with a preset, desired soilrigidity and/or, in particular, a desired modulus of elasticity, andwhich allows the determination of mechanical data for the soil to begraded and tampered, or the graded and tampered soil.

The object of the invention is realized in that, in contrast to patentWO 95/10664, reliance is not placed on the local phase position of amaximum oscillation amplitude of a grading and tampering or measuringdevice, but instead reliance is placed on the temporal phase of theexciting oscillation of the eccentric(s) in relation to the phase of theexcited oscillation of the soil grading and tampering and/or measuringsystems, which is identical to the oscillation of the grading andtampering and/or the measuring devices. Also contrary to WO 95/10664,work is performed in the resonant range of an oscillation system, whichconsists of the grader and tamper or measuring device, acting upon thesoil that is to be compacted (or has been compacted), and the soil.Although the soil grader and tamper apparatus described in EP-A 0 459062 operates in the resonant range of its grader and tamper device, itis unable, however, to determine the soil rigidity C_(B), which isreached with the compacting process, and is therefore not able tooptimize the compacting process on the basis of these establishedvalues.

BRIEF DESCRIPTION OF THE DRAWINGS

To illustrate the invention, the following figures will describe a soilgrader and tamper apparatus according to the invention. The soil graderand tamper apparatus includes a measuring device according to theinvention for the purpose of determining the mechanical data that areessential for the compacting process. They show:

FIG. 1 a schematic depiction of a double tandem vibrating roller withcenter pivot steering, which allows soil grading and tampering accordingto the invention,

FIG. 2 a mechanical equivalent circuit diagram, in terms of oscillation,of the soil grader and tamper apparatus described in FIG. 1,

FIG. 3 a signal block wiring diagram for implementing the soil gradingand tampering according to the invention,

FIG. 4 a standardized oscillation amplitude of the soil grader andtamper device (ordinate) in accordance with FIG. 2 that isinterdependent on a standardized oscillation frequency of the unbalance(abscissa), which excites the oscillation.

FIG. 5 the position of a soil element to be compacted in the ground,

FIG. 6 a compacting force that acts upon the soil element shown in FIG.5,

FIG. 7 a start-up procedure of a soil grader and tamper device in orderto achieve an optimal point of operation shown in a depiction analogousto that in FIG. 4, and

FIG. 8 a schematic depiction of a gearing unit for driving twounbalances of the soil grader and tamper device with adjustable momentof inertia.

DETAILED DESCRIPTION OF THE INVENTION

The double tandem vibrating roller 1 with center pivot steering, shownin FIG. 1, features a front surface and a back surface 3 a and 3 b thatserve as the ground compacting devices. In the following descriptionsonly the one or the other of the two surfaces 3 a and 3 b will beconsidered, and both are designated with the reference number 3, ifthere is no difference between front and back surface 3 a and 3 b. Acoupling between the two surfaces 3 a and 3 b in the context of thedouble tandem vibrating roller 1 described here, for example, is notrelevant for the operating performance.

The surface 3, as shown schematically in the FIGS. 2 and 3, features arotating unbalance with adjustable static unbalance moment m_(u)·r_(u).The unbalance moment is adjusted by modifying the radial unbalancedistance r_(u) of the unbalance 5. Adjusting the moment of inertia andof the frequency f is described below. To simplify the followingremarks, let us assume the mass m_(u) of the unbalance is arrangedpunctiformally, rotating at a distance of r_(u) from the axis ofrevolution 7 of the surface 3. The static unbalance moment is thereforem_(u)·r_(u)[kg·m]. An acceleration recorder is positioned verticallyabove the axis of revolution 7, on the side of a support bracket 9 ofthe surface holding fork 10. The acceleration recorder 11 is able tomeasure the acceleration values of surface 3 in a vertical direction.The acceleration recorder 11 is connected with an arithmetic unit 12 interms of signals, which determines the oscillation amplitude a of thesurface 3 by performing double integration. The surface holding fork 10is connected with the machine chassis 15 by way of spring and dampingelements 13 and 14. The spring and damping elements 13 and 14 aredesigned in such a way that the dynamic forces inside the dampingelement 14 are considerably smaller than the static forces.

With the method according to the invention for the purpose of achievingoptimal, in particular, homogeneous ground compacting, the movementand/or the acceleration of the surface 3 is measured with theacceleration recorder 11, as indicated above. The vibration of thesurface 3, excited by the unbalance 5, can be expressed mathematicallywith the following equation [1]:

X_(d)(t)=a _(½) cos [(Ω/2)t+δ_(½) ]+a ₁ cos [Ωt+δ₁ ]+a_({fraction (3/2)}) cos [(3 Ω/2)t+δ_({fraction (3/2)})

]+a ₂ cos [2 Ωt+δ₂ ]+a _({fraction (5/2)}) cos [(5Ω/2)t+δ_({fraction (5/2)}) ]+a ₃ cos [3 Ωt+δ₃]

In this formula the index 1 indicates an allocation to values, whichhave the same radian frequency Ω (Ω=2 πf, which f being the frequency ofthe unbalance 5), as the exciting vibration of the unbalance 5. ½ refersto half the radian frequency Ω, {fraction (3/2)} refers to one and onehalf of the radian frequency, and {fraction (5/2)} refers to two and onehalf of the radian frequency Ω. a is the maximum amplitude value of therelevant partial oscillation. δ refers to the allocation of partialoscillations to each other in terms of phases.

With the Fourier analysis, and in accordance with the above equation,the partial frequencies can be determined by the arithmetic unit 12 onthe basis of the acceleration signal. Depending on the requiredcompacting procedure, the static unbalance moment of the unbalance 5 andits frequency f is now adjusted differently:

a) If the surface 3 always maintains contract with the ground,essentially, only the rotational frequency 1·f of the surface isdetermined with the Fourier analysis. This compacting procedure iscalled load operation.

b) If the surface 3 periodically lifts off the ground, which incomparison to a) results in more effective compacting, the Fourieranalysis is used to determine harmonic oscillations, i.e. radianfrequencies of 2Ω, 3Ω, . . . with drastically decreasing maximumamplitudes. The lift-off of the surface 3 from the soil ischaracteristic of the optimal mode of operation because in this case theforces transferred upon the soil are more effective than in case a),which results in more effective compacting.

c) If the machine, i.e. the entire roller 1, shows signs of jumping,which means the machine chassis 15 is beginning to exhibit vibrationsaround its steady position, the upper harmonic waves are joined byoscillations with half the exciting radian frequency Ω of the unbalance5, i.e. plus (½) Ω, ({fraction (3/2)}) Ω, ({fraction (5/2)}) Ω, . . .This condition is not stable, and may potentially loosen the graded andtampered soil. Moreover, the machine chassis 15 may begin to vibratearound its longitudinal axis.

In accordance with the equivalent circuit diagram in FIG. 2, the soil20, which is to be graded and tampered, is depicted as a spring 17 and adamping element 19. This means a soil grading and tampering system whichconsists of a surface 3 with oscillation exciting unbalance 5, thespring element 17, and the damping element 19 of the soil 20, that is tobe compacted, and the spring element 13 and the damping element 14between surface 3 and machine chassis 15, shows signs ofself-oscillation. This is confirmed by the measurement curves shown inFIG. 4. The abscissa represents the oscillation radian frequency Ω ofthe surface 3, and the ordinate represents the measured maximumoscillation amplitude. However, the oscillation radian frequency Ω isstandardized to the resonant frequency w₀ of the soil grading andtampering system, and the value a is standardized to a value a₀. Thestatic unbalance moment is the curve parameter [the product of apunctiformally arranged, imagined unbalance mass m_(u) and the radiandistance r_(u) to the axis 7]. The unbalance moment of the curve 21 a issmaller than the unbalance moment of the curve 21 b, etc. Above curve 23the roller 1 begins to jump [case scenario c]. Therefore, duringcompacting operation the curve 23 must not be exceeded. The group of theresonance curves 21 a through 21 d represents an essentialidentification value with respect to the behavior of the soil gradingand tampering system during operation. As shown below, the variousinfluences of the machine parameters and the basic step-by-step processof the compacting operation can be derived from the curves. Compactingis optimal when the soil grading and tampering system, consisting of thecompacting device that is to act upon the soil to be compacted 20, andthe actual soil to be compacted 20, resonates. Optimal operation isreached when the process can be carried out with the greatest speed andthe least energy.

The resonant frequency w₀ of the soil grading and tampering system isthe square root of the quotient of the soil rigidity C_(B) [MN/m] andthe weight m_(d) [kg] of surface 5:

W₀=(c_(B)/m_(d))^(½)

In the above equation a share of the respective wheel support as well asmathematical “shares for the soil” must be added to the weight of thesurface 5. However, at a maximum these additional shares are only 10% ofthe surface's net weight. Preferably, these shares are determined bytrial and error and may be neglected for the purpose of a generalapproximation. Normally, the soil rigidity C_(B) is between 20 MN/m and130 MN/m. The soil rigidity is established according to the invention,as described below. The easiest way to measure the resonant frequency w₀is by running the device across the soil 20 with a small staticunbalance moment in accordance with curve 21 a. The frequency of theunbalance 5 at the maximum curve value of 25 of a/a₀ indicates theresonant frequency w₀. The standardized amplitude value of a /a₀=1 is atthat point where the curve 27, which connects the maximum values of thecurves 21 a through 21 d,starts going off to the left. The amplitudevalue of a₀ can be approximated based on the following formula

a ₀=(m _(f) +m _(d))g/c _(B)  [2]

provided the surface 3 does not lift off (case scenario b). However,this is not the case here. m_(f) is the load of the machine chassis 15per surface 3. g is the Earth's acceleration due to gravity with g≈10.

A position sensor 29 is arranged, fixed in relation to the supportbracket 9, next to the acceleration recorder 11, and it determines thetime the rotating unbalance 5 passes through its minimum point(=direction of compacting). Passing this point is identical with thepoint in time the maximum unbalance force is directed against the soil20. The maximum force acting upon the soil 20, is transferred by thesurface 3 into the soil 20; this process takes place accompanied by aphase displacement at an angle of ø. This means, in effect, that thephase displacement ø reflects the position of the exciting oscillationfrom the unbalance 5 in relation to the oscillation of the soil gradingand tampering system.

Maximum compacting force in the soil 20 is achieved if the soil gradingand tampering system resonates. Resonance of the grading and tamperingsystem always occurs at the maximum values of the curves 21 a through 21d,which are located on curve 27. If resonance occurs, there is also aphase displacement of the exciting oscillation system by the unbalance 5in relation to the soil grading and tampering system, with ø=90°. Thismeans optimal compacting is achieved with roller parameters [staticunbalance moment m_(u)·r_(u) and unbalance rotation radian frequency Ω]that allow operation on the curve 27. The resonance curves 21 a through21 d in FIG. 4 are recorded with constant soil characteristics. The soilcharacteristics, alternatively represented by spring element 17 anddamping element 19 in FIG. 2, are changeable which is why the positionof the resonance curves 21 a through 21 d may also change. As depictedin FIG. 4, the oscillation amplitude, responsible for compacting thesoil 20, changes considerably in the below-resonance range [oscillationradian frequency Ω is smaller than the resonance frequency, phase angleø is smaller than 90°]; however, in the above-resonance range[oscillation radian frequency Ω is larger than the resonance frequency,phase angle ø is larger than 90°] it changes relatively little.Consequently, for stable grading and tampering operation theabove-resonance range should be chosen, and the phase angle ø should beadjusted to a value of between 95° and 110°, preferably 100°.

The adjustment of the phase angle ø is accomplished, with preset staticunbalance moment m_(u)·r_(u),by reducing the rotation radian frequency Ωof unbalance 5. For example, on the resonance curve 21 d movement occursin the direction of the arrow 35. Naturally, the range in which theroller lifts off, characterized by the area above curve 23, must beavoided. Penetration into that range will be felt by the roller operatorbecause the vibration behavior of the roller 1 will change. In terms ofmeasuring technique, as indicated above, oscillations with half thefrequency [and odd multiples] of the rotation radian frequency Ω of theunbalance 5 will occur at that point. This unstable [lift-off] operationmay also be ascertained based on the fact that sequential oscillationamplitudes of the surface 3 exhibit different heights.

To achieve maximum grading and tampering results, the compactingamplitude of the surface 3 must be chosen as large as possible. Forachieving a preset soil modulus of elasticity E or a preset soilrigidity C_(B), the arithmetic unit 12 and adjusting unit 36automatically set the necessary amplitude, as described further below.

The travel speed v of the roller 1 is also adjusted for a regularcompacting operation per unit distance traveled, despite a variablerotation radian frequency Ω of the unbalance 5. The speed variabledepends on the type of layer that is to be compacted. Due to a lowrotation radian frequency Ω, a non-consolidated layer requires a slowertravel speed v than a consolidated layer. For example, for anon-consolidated layer the travel speed is v_(u)=3 km/h with a rotationfrequency of f_(u)=30 Hz, and for a consolidated layer the travel speedis v_(g)=4.5 km/h with a rotation frequency of f_(g)=45 Hz.

A soil element 37, as depicted in FIG. 5, depth of z₀, “sees” atwo-surface roller 1 with a speed of v pass by during the compactingprocess. Depending on the location of the two surfaces 3 a and 3 b thatroll across the soil element 37, the latter experiences, in accordancewith FIG. 6, a different load peak 39. The two load processes for thetwo surfaces 3 a and 3 b, with a pulse draw 40 a originating at thesurface 3 a and a pulse draw 40 b originating at the surface 3 b, can belinearly superimposed. Their effect is cumulative. Depending on theoscillation amplitude a of the soil grading and tampering system, theaxis distance d of the two surfaces 3 a and 3 b, and the depth z₀ of thesoil element 37 in question, a zone of overlap 41 may result, throughwhich the ground element 37 receives parts of the loads from thesurfaces 3 a and 3 b. During operation, the time distance t_(s) of thepartial loads acting upon the soil element 37 should be constant inorder to always achieve consistent compacting quality. As describedbelow, when the soil rigidity C_(B) increases the roller 1, which iscontrolled according to the invention, will operate with a higherrotation radian frequency Ω which, consequently, results in an increaseof the speed travel v. This means the compacting process is carried outwith increasing speed.

In contrast to rollers and compacting procedures known in the art (e.g.WO 95/10664), grading and tampering is no longer carried out only inrelation to a constant modulus of elasticity in shear but with a preset,preferably constant soil rigidity C_(B), and, if necessary, with apreset constant modulus of elasticity E. With rollers and compactingmachinery in the past it was always assumed that at least minimumcompacting, as defined by the soil rigidity C_(B) or the ground modulusof elasticity E could be achieved. The tremendous differences betweenminimum and maximum grading and tampering, resulting from the methodknown in the art, lead to the commonly known, however undesired,irregular sinking and development of unevenness of, for example, roadsurfaces. With the invention these differences will be avoided.

In contrast, the method according to the invention envisions compacting,for example, with a constant modulus of elasticity E. In contrast to thesoils known in the art, which are compacted for minimum soil rigidity, aconstant soil modulus of elasticity E results in considerably betterlong-term stability. It should be reiterated here that compacting iscarried out on the basis of both, the preset soil rigidity C_(B) and thepreset soil modulus of elasticity E. For example, a soil 20 of a roadconstruction, compacted with a constant modulus of elasticity, will sinkevenly while it ages due to the traffic volume, and will therefore havea level surface for much longer than a road compacted in accordance withthe state of the art. Roadways that were graded and tampered inaccordance with the method known in the art become uneven over time dueto non-homogeneous compacting; they show superficial tears and, thus,become vulnerable to destruction due to traffic and weather influences.

According to the invention, the soil modulus of elasticity E isconstantly determined by roller 1, and the machine parameters areconstantly adjusted; however, caution should be exercised that no dipsare left behind, i.e. the soil's surface 42 is already well compacted atthat point. In practical application, the exact soil modulus ofelasticity E is not important until the grading and tampering process isconcluded. At that time, however, the soil surface (42) has already beensufficiently compacted. The soil modulus of elasticity formula E can bederived from the following formula [3]: $\begin{matrix}{E = {{C_{B} \cdot \frac{2( {1 - \mu^{2}} )}{L \cdot \pi}}( {1.89 + {\frac{1}{2}{\ln \lbrack \frac{\pi \cdot L^{3} \cdot E}{16( {1 - \mu^{2}} ){( {m_{f} + m_{d}} ) \cdot g \cdot R}} \rbrack}}} )}} & \lbrack 3\rbrack\end{matrix}$

The above equation results from a postulated continuum mechanicalperspective of a curved body which is in contact with an elastic,semi-infinite area.

Since the value of interest with respect to the soil modulus ofelasticity E appears on both sides of the above equation, its value mustbe determined with a simple iteration. To begin the calculation, on theright side of the equation, for E is put in

E[MN/m²]=2.3 [1/m]·C_(B)[MN/m]  [4]

The soil rigidity C_(B) is determined by the arithmetic unit 12 with theassistance of the formulas a below, because that unit knows all values,or said values were set by it.

During load operation [case scenario a)], i.e. there is no lift-off bythe surface 3 (this operational status applies for the amplitudes up toa/a₀=1), the ground rigidity C_(B) is determined with the formula$\begin{matrix}{C_{B} = {\Omega^{2} \cdot \lbrack {m_{d} + \frac{m_{u} \cdot r_{u} \cdot {\cos (\varphi)}}{a}} \rbrack}} & \lbrack 5\rbrack\end{matrix}$

If the surface 3 lifts off, which is registered by the arithmetic unit12 based on the occurrence of radian frequencies with 2 Ω, 3 Ω, . . .the arithmetic unit calculates the soil rigidity C_(B) with the formula$\begin{matrix}{C_{B} = \frac{F( {{{at}\quad å} = 0} )}{\lbrack {1 - {\cos ( {{\pi^{2}/2}K} )}} \rbrack \cdot a}} & \lbrack 6\rbrack\end{matrix}$

while

F=−m_(d)·ä+m_(u)·r_(u)·Ω²·cos ø+(m_(f)+m_(d))·g  [7]

and $\begin{matrix}{K = \frac{F_{m\quad a\quad x}}{( {m_{f} + m_{d}} ) \cdot g}} & \lbrack 8\rbrack\end{matrix}$

{dot over (a)} is calculated by integration of the value measured withthe acceleration recorder 11. {dot over (a)} is the vertical speed ofthe surface 5. This is the surface speed that changes according to time,and should not be confused with the travel speed v. {dot over (a)}=0,i.e. a speed zero of the surface 5 is always reached in both the upperand lower oscillation cuspidal points. a is the value established by theacceleration recorder 11. The static imbalance moment m_(u)·r_(u)[kg m]in the above formula can be determined on the basis of the unbalance 5data. How to establish the phase angle ø has been described above. m_(d)[kg] is known as the weight of the respective surface 3. Ω is adjustedas rotation radian frequency of the surface 3, and is therefore known.The maximum oscillation excursion a of the surface 3 can also bedetermined.

In formula [3] the transversal contraction number of the sub-soil is setat μ=0.25 (it is between 0.20 and 0.30). L [m] is the width of thesurface 3, (m_(f)+m_(d)) the load each surface 3 a and/or 3 b iscarrying, plus the respective weights of surfaces 3 a and/or 3 b, R [m]is the radius of the surface 3, g [=10 m/s²] the Earth's accelerationdue to gravity, and in the natural logarithm. Thus, all values forautomatic determination of the soil rigidity C_(B) are known, or can bedetermined with the arithmetic unit 12, which means that the modulus ofelasticity E can also be established with the assistance of thearithmetic unit 12.

To arrive at the above formula [3] we assume that two elastic rolls aretouching. The first roll has a modulus of elasticity E₁, a radius R₁ anda transversal contraction number μ₁. The second roll has a modulus ofelasticity E₂, a radius R₂, and a transversal contraction number μ₂.Both rolls have a length L. For the surface pressure p [N/m²] betweenthe two rolls, therefore, results

$\begin{matrix}{p = {\frac{4 \cdot P}{\pi \cdot L \cdot b} \cdot ( \lbrack {1 - {( {4 \cdot y^{2}} )/b^{2}}} \rbrack )^{\frac{1}{2}}}} & \lbrack 10\rbrack\end{matrix}$

P is the force acting on the first roll, b is the width of the contactsurface ( L·b), in relation to which the two rolls are touching due toelastic deformation, and y is the running coordinate vertical to theaxis of the roll, and with the origin of coordinates on the axis of theroll.

As transition for a roll compacting the soil (surface) we assume thatthe soil is the second roll described above. The radius R₂=∞ is set. Inaddition, the modulus of elasticity E₁ of the first roll is considerablylarger than the E₂ of the soil. Therefore, it is valid

E ₁>>E₂.

Thus, in relation to E₂, it can be set E₁→∞

The force P which acts upon the first roll is, in the context of a soilgrading and tampering apparatus, a function of time. It is nottemporally constant. The force P is identical with the soil reactionforce F in the equations [6], [7], and [8]. Establishing the temporalmean with regard to the force P during one rotation of the surface 3leads to $\begin{matrix}{\frac{1}{T} = {{\int_{0}^{T}{P \cdot \quad {t}}} = {( {m_{f} + m_{d}} ) \cdot g}}} & \lbrack 11\rbrack\end{matrix}$

Thus, in equation [10] it is set P=(m_(f)+m_(d))·g. Solving the equation[10] with respect to b results therefore in $\begin{matrix}{{b\lbrack m\rbrack} = ( \lbrack {( {16/\pi} ) \cdot \frac{( {1 - \mu_{2}^{2}} )}{E_{2}} \cdot \frac{{R_{1}( {m_{f} + m_{d}} )} \cdot g}{L}} \rbrack )^{\frac{1}{2}}} & \lbrack 12\rbrack\end{matrix}$

μ₂ and E₂ are the transversal contraction and the modulus of elasticityof the soil.

Due to the elasticity of the soil E₂, when applying the force P, the midpoint of the first roll approaches the soil's surface. Thisapproximation δresults with regard to $\begin{matrix}{{\delta \lbrack m\rbrack} = {\frac{P}{L} \cdot \frac{1 - \mu_{2}^{2}}{E_{2}} \cdot {E( {b/L} )}}} & \lbrack 13\rbrack\end{matrix}$

Since the width of the contact surface (L·b) is considerably smallerthan its length L (b<<L) it is valid that${\ominus ( {b/L} )} \approx {\frac{2}{\pi} \cdot \lbrack {1.89 + {\ln ( {L/b} )}} \rbrack}$

Also valid is (spring equation)

F=C_(B)·δ

and therefore $\begin{matrix}{C_{B} = {{\frac{F}{\delta} \equiv \frac{P}{\delta}} = \frac{L \cdot E_{2}}{( {1 - \mu_{2}^{2}} ) \cdot {\ominus ( {b/L} )}}}} & \lbrack 14\rbrack\end{matrix}$

therefore it follows $\begin{matrix}{E_{2} = {\frac{( {1 - \mu_{2}^{2}} )}{L} \ominus {( {b/L} ) \cdot C_{B}}}} & \lbrack 15\rbrack\end{matrix}$

Now b is replaced with the above value${\ominus ( {b/L} )} = {\frac{2}{\pi} \cdot \lbrack {1.89 + {\frac{1}{2}{\ln \lbrack \frac{\pi \cdot E_{2} \cdot L^{3}}{16{( {1 - \mu_{2}^{2}} ) \cdot R_{1} \cdot ( {m_{f} + m_{d}} ) \cdot g}} \rbrack}}} }$

If equation [16] is put into equation [15], the above equation [3]results, with R₁=R.

For optimum grading and tampering of the soil areas to be compacted, theroller 1 must run across them several times. Due to the fact that,normally, the soil in question is not pre-compacted, the first and/orfollowing grading and tampering runs will result in maximum compacting.

Adjusting the optimal unbalance radian frequency Ω as well as of theoptimal static unbalance moment is described in FIG. 7, while, analogousto FIG. 4, the standardized unbalance radian frequency Ω [Ω/w₀] isrepresented as abscissa value, and the standardized maximum amplitude a[a/a₀] of the unbalance 5 is represented as ordinate value. At thebeginning of a soil grading and tampering process the unbalance 5 showsa minimum distance r_(u0)to the rotation axis 7 [static unbalance momentm_(u)·r_(u0)]. The rotation radian frequency Ω of the unbalance 5 isincreased, starting from standstill, to the value Ω₀ located above theresonance of the soil grading and tampering system referred to above.The respective travel speed v of roller 1 is adjusted, in accordancewith the above comments, to the rotation frequency f of the unbalance 5.The amplitude a of the surface 3 is interdependent on the rotationradian frequency Ω in correspondence with the curve 43 a. The resonanceof the soil grading and tampering system is located in point 45. Thisresonance point is exceeded, based on the tolerance reasons explainedabove, until the phase angle ø between surface oscillation and unbalanceoscillation is approximately 100° [point 47]. In a next step the staticunbalance moment is increased, by increasing the radial distance ofr_(u0) to r_(ul)[m_(u)·r_(ul)]. Due to the fact that the staticunbalance moment is increased while the unbalance rotation frequency fremains unchanged, the phase angle ø increases to a value of above 100°,as seen by the distance of the new adjustment point 50 from theresonance curve 49 (analogous to curve 27 in FIG. 4). In a next step therotation radian frequency of the unbalance 5 is lowered from Ω₀ to Ω₁,while the static unbalance moment remains constant [m_(u)·ru_(i)], untilthe phase angle ø returns to 100°. The radial distance r_(u) and therotation radian frequency Ω are now changed alternately until the roller1 starts to lift off. This “lift-off” is, in accordance with thecomments above, noticeable at the point when odd multiples of one halfof the unbalance rotation frequency occur [when curve 52 is exceeded].The static unbalance moment m_(u)·r_(u) is reduced in order to reach thestable curve point 51. It is also possible to lower the unbalance radianfrequency Ω, however, this type of adjustment is difficult to carry outbecause with this alternative two values change, i.e. the radianfrequency Ω and the moment of inertia. The machine parameters allocatedto curve point 51 define the conditions under which maximum grading andtampering operation is realized. The curve 53 in FIG. 7 represents theoptimal adjustment curve which always ensures a phase angle ø of 100°.

After the first runs, for as long as the soil maintains its plasticproperties, maximum compacting performance is reached. The plasticproperties are derived from the measured values. In the “plastic range”the soil rigidity C_(B) can only be approximated. Aware of the fact thatthe determination of the soil modulus of elasticity is flawed as longthe sub-soil still exhibits plastic properties, it is calculatedfollowing the above explanations. When approximately 90% of the requiredsoil elasticity value is reached, the plastic range is exceeded and thecontrol adjusts, using the above calculation procedure, the staticunbalance moment m_(u)·r_(u) and the unbalance rotation frequency f(unbalance rotation radian frequency Ω) in such a way that a preset soilmodulus of elasticity E is reached. Using the formulas [3] and [5] thearithmetic unit 12 is able to determine during compacting the respectivesoil modulus of elasticity E that has already been achieved, and basedon these values, for further compacting, the relevant machine parameterscan be adjusted, such as static unbalance moment m_(u)·r_(u) unbalancefrequency f and travel speed v. The adjustments are effected during theprocess. Adjusting the travel speed v is accomplished easily andrapidly. However, in order to adjust the static unbalance momentm_(u)·r_(u) in the fractional second range to a preset, determined valuee.g. the process described below is used.

Instead of changing, as indicated above, the radial distance r_(u) ofthe unbalance mass, two unbalances 56 and 64 running in the samedirection can be used, and their mutual radial distance is adjusted bymeans of a planetary gearing. If the radial distance is 180°, theeffective, total unbalance value is zero. At 0° the unbalance value isat its maximum. Using angle values of between 0° and 180° allintermediate values between zero and maximum unbalance mass can beadjusted.

The planetary gear 53, depicted schematically in FIG. 8, serves as adrive mechanism for the two unbalances 56 and 64, which run in the samedirection, and the mutual locations of which can be modified in order toadjust the static unbalance moment m_(u)·r_(u). In contrast to the aboveremarks, it is no longer the radial distance r_(u) of an punctiformallyimagined eccentric mass that is adjusted, but, with an unchanged radialdistance r_(u), the effective unbalance mass m_(u) is now adjusted. Theadjustments according to FIG. 7 are carried out on the basis of [Ω₀,m_(u0)·r_(u0)] at the curve point 47 for the following curve points with[Ω₁, m_(u1)·r_(u0)] instead of [Ω₀, m_(u)·r_(u1)] at the adjustmentpoint 50, with [Ω₁, m_(u1)·r_(u0)] instead of [Ω₁, m_(u)·r_(u1)], [Ω₁,m_(u2)·r_(u0)] instead of [Ω₁, m_(u)·r_(u2)]etc. With the planetarygearing 53, depicted in FIG. 8, unbalance mass adjustments are possiblein fractions of a second.

The planetary gearing shown in FIG. 8 is driven by a drive 54 via aspindle 55, which acts directly on the unbalance 56 and without anyintermediate gears. On the spindle 55 a tooth lock washer 57 is arrangedwhich acts via a toothed belt 59 on a tooth lock washer 60. The toothlock washer 60, on the other hand, acts in conjunction with a gearingpart 61. The gearing part 61 features three meshing gears 63 a, 63 b and63 c; the gear 63 a and the tooth lock washer 60 are connected withtorsional strength. The axis of the gear 63 b can be turned radially inrelation to the rotation axis of the gear 63 a. The twisting angle is ameasure for the radial torsion of the two unbalances 56 and 64, andthereby a measure for the effective total unbalance mass, or theeffective static unbalance moment m_(u0)·r_(u) to m_(u3)·r_(u). On theaxis 65 of the gear 63c is located a gear 66 which meshes with a gear 69located on a hollow shaft. The hollow shaft 67 acts in conjunction withthe second unbalance 64.

Since one of the two unbalances 56 and 66 is driven directly, and onlythe unbalance 64 is driven by the planetary gearing 53, the latter onlyhas to transfer half of the torque. Reference point for determining thephase angle ø is the bisecting line between the centers of gravity ofthe unbalances 56 and 64.

It is not necessary to let the two unbalances run in the same directionwith identical rotation frequencies Ω. With a corresponding selection oftooth lock washers 57 and 60 and/or the gears 66 and 69, it is possibleto let one of the two unbalances run with double the rotation frequency.

The gearing described above, and as shown in FIG. 8, can also bereplaced with superimposed gearing that acts identical but isconstructed differently. For example, good results were achieved withthe so-called “harmonic drive gearing” which reaches high one-step speedincreasing ratios with only three components [wave generator, circularspline, and flex spline]. With this gearing, the circular spline is arigid steel ring with internal toothing, which meshes into the externaltoothing of the flex spine in the area of the large elliptical axis ofthe wave generator. The flex spline is an elastically distortionable,thin-walled steel bushing with external toothing featuring a smallerpartial circle diameter than the circular spline. It has therefore e.g.two fewer teeth with regard to its overall circumference. The wavegenerator is an elliptical disc with an open thin ring ball bearingwhich is inserted into the flex spine and deforms it elliptically.During the turns of the wave generator the toothing meshes with thelarge elliptical axis. After the wave generator has completed a 180°turn, a relative movement by one tooth occurs between the flex splineand the circular spline. After each turn that the wave generatorcompletes, the flex spline, as drive element, turns by two teeth in theopposite direction of the drive. When this gearing is used themechanical assembly is extremely compact.

If fill-in material is to be compacted at a construction site, it isrecommended that before the material to be compacted is deposited, toestablish or to test the rigidity C_(B) of the sub-soil by one machinerun across the soil. Of course, the soil modulus of elasticity E canalso be determined. If the sub-soil already contains weak points, thefill-in material cannot be compacted to the extent that is necessary.

Instead of using rotating unbalances, the use of vertically oscillatingunbalances, designed as piston-cylinder units, is also possible. Tograde and tamper, the surfaces can be rolled across the soil 20, but itis also possible to move a vibrating plate across the soil 20.

The measuring apparatus according to the invention differs from the soilgrading and tampering apparatus only insofar as the apparatus that actsupon the soil and forms an oscillation system with the latter does notessentially effect the compacting of the soil, which is in contrast tothe grading and tampering device of the soil grading and tamperingapparatus. This means that during the measurement procedure the forcethat acts upon the soil is reduced. Also, while measuring a smaller massof the oscillating force is usually selected. The measuring apparatusaccording to the invention can be combined with grading and tamperingdevices known in the art in order to improve soil compacting operationalso in conjunction with that machinery.

What is claimed is:
 1. A method for measuring a mechanicalcharacteristic of a soil using a soil compacting device and anarithmetic unit, comprising: periodically compacting the soil using thesoil compacting device so as to make the soil compacting device and thesoil vibrate; using the arithmetic unit to analyze the vibration of thesoil compacting device and the soil together as a single oscillatorysystem having a characteristic resonant frequency Ω; and dynamicallyadjusting the compacting of the soil so that the single oscillatorysystem resonates or oscillates at a frequency exceeding thecharacteristic resonance frequency Ωn by a preset frequency; whereindynamically adjusting the compacting of the soil comprises using thearithmetic unit to automatically adjust an oscillation exciting forcefor driving the soil compacting device, a period frequency of theoscillation exciting force, and a phase angle (ø) between oscillation ofthe soil compacting device and vibration of the single oscillatorysystem; so that, in view of a mass (m_(d)) of the soil compacting deviceand a static weight load (m_(f)) of the soil compacting device, adesired soil rigidity (C_(B)) is achieved.
 2. The method defined inclaim 1, further comprising: determining a vibration amplitude (a) ofthe single oscillatory system by calculating a vertical movement of thesoil compacting device; adjusting a phase angle (ø) between anoscillation of the soil compacting device and an oscillation of thesingle oscillatory system; and generating an oscillation exciting forcefor driving the soil compacting device with an eccentrically locatedmass having a static unbalanced moment (m_(u)·r_(u)) which is controlledby the arithmetic unit.
 3. The method for compacting as defined in claim2, wherein calculating a vertical movement of the soil compacting deviceincludes measuring an acceleration of the soil compacting device with anacceleration gauge.
 4. The method for compacting as defined in claim 2,wherein adjusting the phase angle (ø) comprises making the phase angle(ø) between 90° and 110° in lead.
 5. The method for compacting asdefined in claim 2, wherein the eccentrically located mass is a rotatingmass.
 6. The method for compacting as as defined in claim 2, comprising:determining if a modulus of elasticity (E) of the soil has reached athreshold value using the arithmetic unit, including determining themodulus of elasticity (E) in terms of one or more of the soil rigidity(C_(B)), the vibration amplitude (a), and the acceleration of the soilcompacting device.
 7. The method as defined in claim 1, furthercomprising: moving the compacting device relatively more rapidly acrossa first soil that has already been graded and tampered to a preset valuethan across a second soil that has yet to be compacted, wherein areduced oscillation exciting force is used to minimize, from acompacting point of view, unnecessary runs.
 8. A method as defined inclaim 1, comprising: grading and tampering non-consolidated materialusing a soil grading and tampering device including the compactingdevice in a first compacting procedure depending on soil characteristicsand compacting conditions, at maximum compacting output, with outputonly being limited by a capacity of the machinery, with an oscillationexciting force automatically adjusted such that no lift-off of the soilgrading and tampering device occurs; and determining the lift-off pointof the soil grading and tampering device using a frequency analysis ofthe vibration of the compacting device based on an occurrence of onehalf of a partial oscillation component in relation to a fundamentaloscillation or based on a comparison of amplitudes of sequentialoscillations of the compacting device up to a preset deviation value. 9.The method as defined in claim 1, further comprising: determining avibration amplitude (a) of the single oscillatory system by calculatinga vertical movement of the soil compacting device, and making a phaseangle (ø) between an oscillation of the soil compacting device and anoscillation of the single oscillatory system between 90° and 110° inlead.
 10. The method as defined in claim 1, further comprising:determining a vibration amplitude (a) of the single oscillatory systemby calculating a vertical movement of the soil compacting device, andgenerating an oscillation exciting force for driving the soil compactingdevice using an eccentrically located mass having a static unbalancemoment (m_(u)·r_(u)) which is controlled by the arithmetic unit.
 11. Themethod as defined in claim 1, wherein the eccentrically located mass isa rotatable eccentrically located mass.
 12. A measuring apparatus formeasuring a mechanical characteristic of a soil, comprising: at leastone soil compacting device in contact with the soil at least some of thetime, the at least one soil compacting device including at least oneoscillating mass which generates a periodic force on the at least onesoil compacting device, the vibration frequency (Ω) of the at least oneoscillating mass being adjustable with a drive; a measuring elementwhich determines a point in time of a maximum oscillation amplitude (a₀)of the soil compacting device; a sensor for identifying a point in timeof a maximum oscillation amplitude of the oscillating mass and anarithmetic unit to analyze the vibration of the soil compacting deviceand the soil together as a single oscillatory system having acharacteristic resonant frequency (Ω), said arithmetic unit dynamicallyadjusting the compacting of the soil so that the single oscillatorysystem resonates or oscillates at a frequency exceeding thecharacteristic resonance frequency (Ω) by a preset frequency, whereindynamically adjusting the compacting of the soil comprises using thearithmetic unit to automatically adjust an oscillation exciting forcefor driving the soil compacting device, a period frequency of theoscillation exciting force, and a phase angle (ø) between oscillation ofthe soil compacting device and vibration of the single oscillatorysystem.